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Math Help - Compound angles HELP!

  1. #1
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    Compound angles HELP!

    Hi I'm new to this, I've been given a question on compound angles and I really don't know how to go about it. Any help would be greatly appreciated:

    Using compound angles prove that Cos(y-pi)+Sin(y+pi/2)=0

    thanks Shaun
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  2. #2
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    Re: Compound angles HELP!

    Hello, Shaun!

    You are expected to know these Compound Angle Identities:

    . . \sin(A \pm B) \:=\:\sin A\cos B \pm \cos A\sin B

    . . \cos(A \pm B) \:=\:\cos A\cos B \mp \sin A\sin V


    Using compound angles prove that: . \cos(x-\pi)+\sin(x+\tfrac{\pi}{2})\:=\:0

    We have: . \cos(x - \pi) \:=\:\cos(x)\cos(\pi) + \sin(x)\sin(\pi)

    . . . . . . . . . . . . . . . . =\;\cos(x)\!\cdot\!(\text{-}1) + \sin(x)\!\cdot\!(0)

    . . . . . . . . . . . . . . . . =\;\text{-}\cos(x)


    We have: . \sin(x +\tfrac{\pi}{2}) \;=\;\sin(x)\cos(\tfrac{\pi}{2}) + \cos(x)\sin(\tfrac{\pi}{2})

    . . . . . . . . . . . . . . . . =\;\sin(x)\!\cdot\!(0) + \cos(x)\!\cdot\!(1)

    . . . . . . . . . . . . . . . . =\;\cos(x)


    Therefore: . \cos(x-\pi) + \sin(x + \tfrac{\pi}{2}) \;=\;\text{-}\cos(x) + \cos(x) \;=\;0

    Thanks from Kosky1
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  3. #3
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    Re: Compound angles HELP!

    Ah thankyou. I had those identities right infront of me! Had a complete mind block
    Thank you ever so much!
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